Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning.

With an extremely refined analysis, Klein shows how modern mathematics obliterates the Greek conception of knowledge and of our relationship with experience, replacing a vision of given shapes given with an articulated symbolically technique.